Simulating chemistry on IBM Q quantum processors
Pauline Ollitrault1, Panagiotis Barkoutsos1, Igor Sokolov1, Ivano Tavernelli1 (*)
1 IBM Research GmbH, Zurich Research Laboratory, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
(*)The authors would like to acknowledge the IBM T.J. Watson Research Center team and the IBM Q team
Within the second quantization formalism of quantum mechanics, we can map the electronic structure Hamiltonian of any molecular system into the corresponding qubit Hamiltonian using either the Jordan-Wigner, the binary-tree or the parity mapping transformations. The implementation of these transformations in the particle-hole (p/h) picture was shown [1] to improve the accuracy and speed of convergence for ground state properties (e.g. energy, dipole moments, etc.). In fact, the shift of the reference wavefunction from the vacuum state to the Nelectron Hartree-Fock (HF) ground state in the p/h picture allows for a more efficient implementation of the wavefunction optimization process. The ground state electronic energy is obtained using the variational quantum eigensolver (VQE) algorithm, where the exponentially hard part of the problem (the sampling of the wavefunction space) and the calculation of the Hamiltonian expectation values are performed in the quantum hardware, while the parameters optimization is done on a classical computer. To this end, the trial wavefunctions are parametrized using two alternative strategies: the hardware-efficient heuristic approach [2] and the Unitary Coupled Cluster expansion [1].
In particular, in this work we illustrate the use of the open source IBM Quantum Information Software Kit (QISKit) [3] to perform ground state energy optimization of relatively simple molecules (hydrogen and water molecules) on a quantum simulator of the IBM quantum hardware (IBM Quantum Experience). We show that QISKit is a valuable tool for quantum chemistry applications on near-term quantum computers.
[1] Panagiotis Barkoutsos, et al. "Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions." To appear soon (2018).
[2] Kandala, Abhinav, et al. "Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets." Nature 549.7671 (2017): 242.
[3] https://qiskit.org/